The approach of using the dissolution theory described earlier to evaluated the dispersion process for furosemide has been reported (20).good agreement between theoretical and experimental dissolution profiles were found whemn furosemide powders were dispersed by ultrasonication in a surpactan solution for allout the smallest of three batches of powder.The mean particle sizes for the batches were 3, 10, and 19 nm whwn particle size was measured after sonication .without sonication ,the particle size were measured to be 108 ,38,and 27 nm corresponding to the post-sonicated measurements of 3, 10, and 19 nm respectively .The relative order of the dissolution rates were also reversed before and after dispersion ,indicating that comparing theoretical profiles with actual profiles would reveal the problem with agglomeration .for the smallest particle size batch of the furosemide that did no agree well with the theoretically calculated dissolution which would exlaint why the actual dissolution rate was slower than predicated by theory (M.M. De Villiers.Personal communication ,2005)
Disintegration ,wetting ,and agglomeration should be understood and addressed by the formulator ,if not more variability in the in vitro / in vivo correlation in likely to result if a patient were to igest something that minght increase the wetting of a drung product that dose not provide a surpactant itself.This whould be analogous to adding a surfactant to the dissolution profile. Againt , theory cant help the formulator identify potential dissolution problems.
The ability of the theory present hereint to simulate a polidisperse powder under nonsink conditions which has been shown in studies that carefully address wetting and dispersion,challenges the conventional wisdom of conducting dissolution under sink condition s.the pollowing example will be based on the physical properties of digoxin ,whose bioavaibility has been shown clinically to be dependent on its particle size(21).this dependency requires that drug particle size be controlled so that dissolution and bioavibilittoy in consistent from bacth to bacth of drung to product.
The question is whether to test dissolution under sink or non sink conditions. Hipothetically ,let it be assumed that the drug particle size spesipication calls for the drug powder to have a geometric mean particle size of 10 nm an a geometric standard deviation of 2. Figure 3 compares the simulated dissolution profile of a 1 mg dose of drug that has a solubility of 0.05 mg/ml,similar in dose solubility to digoxin .profiles compare the simulated dissolution of a 1 mg dose in 900 or 90 ml of water for drug powder with geometric mean particle sizes of a 10 and 20 nm. Both with geometric standars deviation of 2. In figure 3 .dissolution is expresend as mass dissolved as a function of time with total dissolution occurring at the dose of 1 mg.the higher and lower solid-line profiles refresent thr dissolution of a 10 and 20 nm powders, respect –ively, dissolving in 900 ml.The higher and lower dash –line profiles referesent the dissolution of 10 and 20 powders, respectively , dissolving in 90 ml.
Figure 3 simulated dissolution of a 1 mg dose with a solubility of 0.0versus 20 m (5 mg/ml in 900 ml ( solid) versus 90 90 ml (dashed lines) for a drug with a mean particle size of 10 m (top two curves )versus 20 m ( bottom two curves).
As expented, issolusion occurs faster in 900 versus 90 ml for both the 10 and 20 nm powders.however , the different is not large and the ability of the simulated dissolution to differentiate the 10 versus 20 nm powder dose not appear to depend on the volume of the water used in the dissolution test. In figure 4 .the same profile are expressed as concentration instead of mass.againt ,the dash line profile in figure 4 are the dissolution profile off drug dissolving in 900 ml of water .with the higher profile being the 10 nm powder and the lower being the 20 nm powder.the two solid-line profiles in figure 4 are the dissolution profile of drug dissolving in 900 ml of water ,with the higher profile being the 10 nm powder and the lower being the 20 nm powder.figure 4 shows .
Figure 4 simulated dissolution as in figure 3 excep only expressed as concentration instead of mass for a 1 mg dose with a solubility of 0.05 mg/ml in 900 ml (solid lines) versus 90 MI (dashed lines ) for drug with a mean particle size of 10 m (second and fourth curves from the top).
That the instrumental analysis would be much easier if dissolution were done il 90 Ml of water because the resulting concentration are 10 times higher .the conclusion of this example is that doing the dissolution testing under nonsink condition in 90 ML of water versus sink conditions in 900 ML dose not affect the ability to differentiate the particle size – dependent dissolution and makes the instrumental analysis of the different easier.
Another advantage of adopting a modeling approach of simulation using a system of numerically solved equations is the ability to expand the model.up to this point .the discussion has focused on describing events, such as dissolution and absorptions, that occur on one side of the Cl membrane with the fate of absorbrd drug left undefined.however , by expanding the system of metabolism,tissue distribution, clearance and exreation ,the blood plasma versus time profile can be simulated in a dynamic way .this allows the coupling of dissolution and pharmacokinetic with the absorbtion rate constant or permeability as the link.leading to an invitro / in vivo correlation.
Figure 5 and following equations will be used to illustrate how dissolution and pharmacokinetics can be condined and dynamic way to provide a mechanistically based in vitro invipo correlation .the top cylinder In figure 5 is meant to refresent the Gi tract . inside the imaginary Gi tract is shown a cylindrical plug on the left is intended to refresent a plung of GI fluid being propelled down the tract by peristalsis.the plung on the right is intended to
Figure 5 a schematic refresentation of the mathimathical model described by equations 26 to 23